On the Finite Population Evolutionary Stable Strategy Equilibrium for Perfect Information Extensive Form Games

This study presents an adaptation of finite population evolutionary stable strategy definition by Schaffer in [1, 2] to perfect information extensive form games. In this adaptation, players reach a finite population evolutionary stable strategy equilibrium by using finite population evolutionary stable strategies which ensure that the game ends up with equal payoffs. We studied the fpESS equilibria of some famous two-player bargaining games such as the ultimatum game, the dictatorship game and a dollar auction game. Not all Perfect Information Extensive form games have an fpESS equilibrium. However, when there exist an fpESS equilibrium in these games, the outcome is a perfectly fair one; that is, all players get equal payoffs.